Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C26 |
| direct product | C2×D11×#97 |
| Fitting | C2×C11×#97 ⋊ C2 |
| Sylow | C11 ⋊ C22×#97 |
680 conjugacy classes of subgroups; only the 365 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 365 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 704 |
280 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D11×#1275, #14643193, D11×#1281, … |
| maximal normal subgroup of | D11×#1275, #14643193, D11×#1281, … |
| maximal quotient of | C2×D11×#322, D11×#1451, C2×#13066902, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 12912);